What is floating point number? What is the difference between Single precision and double precision floating point numbers? What is a representation for Zero in IEEE 754 single precision standard. Represent (-23456.05)10 and (0.00025)10 in IEEE 754 single precision format.
Answers
In computing, floating-point arithmetic (FP) is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision. For this reason, floating-point computation is often found in systems which include very small and very large real numbers, which require fast processing times. A number is, in general, represented approximately to a fixed number of significant digits (the significand) and scaled using an exponent in some fixed base; the base for the scaling is normally two, ten, or sixteen. A number that can be represented exactly is of the following form:
{\displaystyle {\text{significand}}\times {\text{base}}^{\text{exponent}},} {\text{significand}}\times {\text{base}}^{\text{exponent}},
where significand is an integer (i.e., in Z), base is an integer greater than or equal to two, and exponent is also an integer. For example:
{\displaystyle 1.2345=\underbrace {12345} _{\text{significand}}\times \underbrace {10} _{\text{base}}\!\!\!\!\!\!^{\overbrace {-4} ^{\text{exponent}}}.} 1.2345=\underbrace {12345} _{\text{significand}}\times \underbrace {10} _{\text{base}}\!\!\!\!\!\!^{\overbrace {-4} ^{\text{exponent}}}.
The term floating point refers to the fact that a number's radix point (decimal point, or, more commonly in computers, binary point) can "float"; that is, it can be placed anywhere relative to the significant digits of the number. This position is indicated as the exponent component, and thus the floating-point representation can be thought of as a kind of scientific notation.